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Periodic solutions of a Cohen-Grossberg-type BAM neural networks with distributed delays and impulses. (English) Zbl 1244.93122
Summary: A class of Cohen-Grossberg-type BAM neural networks with distributed delays and impulses are investigated in this paper. Sufficient conditions to guarantee the uniqueness and global exponential stability of the periodic solutions of such networks are established by using suitable Lyapunov function, the properties of $M$-matrix, and some suitable mathematical transformation. The results in this paper improve the earlier publications.

MSC:
93D05Lyapunov and other classical stabilities of control systems
92B20General theory of neural networks (mathematical biology)
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References:
[1] Z. Huang and Y. Xia, “Exponential periodic attractor of impulsive BAM networks with finite distributed delays,” Chaos, Solitons and Fractals, vol. 39, no. 1, pp. 373-384, 2009. · Zbl 1197.34124 · doi:10.1016/j.chaos.2007.04.014
[2] S. Townley, A. Ilchmann, M. G. Weiß et al., “Existence and learning of oscillations in recurrent neural networks,” IEEE Transactions on Neural Networks, vol. 11, no. 1, pp. 205-214, 2000. · doi:10.1109/72.822523
[3] M. A. Cohen and S. Grossberg, “Absolute stability of global pattern formation and parallel memory storage by competitive neural networks,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 13, no. 5, pp. 815-826, 1983. · Zbl 0553.92009 · doi:10.1109/TSMC.1983.6313075
[4] B. Kosko, “Bidirectional associative memories,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 18, no. 1, pp. 49-60, 1988. · doi:10.1109/21.87054
[5] J. Sun and L. Wan, “Global exponential stability and periodic solutions of Cohen-Grossberg neural networks with continuously distributed delays,” Physica D, vol. 208, no. 1-2, pp. 1-20, 2005. · Zbl 1086.34061 · doi:10.1016/j.physd.2005.05.009
[6] Y. Li, “Existence and stability of periodic solutions for Cohen-Grossberg neural networks with multiple delays,” Chaos, Solitons and Fractals, vol. 20, no. 3, pp. 459-466, 2004. · Zbl 1048.34118 · doi:10.1016/S0960-0779(03)00406-5
[7] C.-H. Li and S.-Y. Yang, “Existence and attractivity of periodic solutions to non-autonomous Cohen-Grossberg neural networks with time delays,” Chaos, Solitons and Fractals, vol. 41, no. 3, pp. 1235-1244, 2009. · Zbl 1198.34139 · doi:10.1016/j.chaos.2008.05.005
[8] Q. Song, J. Cao, and Z. Zhao, “Periodic solutions and its exponential stability of reaction-diffusion recurrent neural networks with continuously distributed delays,” Nonlinear Analysis. Real World Applications, vol. 7, no. 1, pp. 65-80, 2006. · Zbl 1094.35128 · doi:10.1016/j.nonrwa.2005.01.004
[9] X. Yang, “Existence and global exponential stability of periodic solution for Cohen-Grossberg shunting inhibitory cellular neural networks with delays and impulses,” Neurocomputing, vol. 72, no. 10-12, pp. 2219-2226, 2009. · doi:10.1016/j.neucom.2009.01.003
[10] Q. Liu and R. Xu, “Periodic solutions of high-order Cohen-Grossberg neural networks with distributed delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 7, pp. 2887-2893, 2011. · Zbl 1221.37215 · doi:10.1016/j.cnsns.2010.10.002
[11] H. Xiang and J. Cao, “Exponential stability of periodic solution to Cohen-Grossberg-type BAM networks with time-varying delays,” Neurocomputing, vol. 72, no. 7-9, pp. 1702-1711, 2009. · doi:10.1016/j.neucom.2008.07.006
[12] Y. Li, X. Chen, and L. Zhao, “Stability and existence of periodic solutions to delayed Cohen-Grossberg BAM neural networks with impulses on time scales,” Neurocomputing, vol. 72, no. 7-9, pp. 1621-1630, 2009. · doi:10.1016/j.neucom.2008.08.010
[13] A. Chen and J. Cao, “Periodic bi-directional Cohen-Grossberg neural networks with distributed delays,” Nonlinear Analysis. Theory, Methods & Applications, vol. 66, no. 12, pp. 2947-2961, 2007. · Zbl 1122.34055 · doi:10.1016/j.na.2006.04.016
[14] X. Li, “Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays,” Applied Mathematics and Computation, vol. 215, no. 1, pp. 292-307, 2009. · Zbl 1190.34093 · doi:10.1016/j.amc.2009.05.005
[15] Y.-t. Li and J. Wang, “An analysis on the global exponential stability and the existence of periodic solutions for non-autonomous hybrid BAM neural networks with distributed delays and impulses,” Computers & Mathematics with Applications, vol. 56, no. 9, pp. 2256-2267, 2008. · Zbl 1165.34410 · doi:10.1016/j.camwa.2008.03.048
[16] J. Principle, J. Kuo, and S. Celebi, “An analysis of the gamma memory in dynamics neural networks,” IEEE Transactions on Neural Networks, vol. 5, pp. 337-361, 1994.
[17] R. S. Varga, Matrix Iterative Analysis, vol. 27, Springer, Berlin, Germany, 2000. · Zbl 0998.65505
[18] K. Li, L. Zhang, X. Zhang, and Z. Li, “Stability in impulsive Cohen-Grossberg-type BAM neural networks with distributed delays,” Applied Mathematics and Computation, vol. 215, no. 11, pp. 3970-3984, 2010. · Zbl 1191.34091 · doi:10.1016/j.amc.2009.12.001
[19] K. Li, “Stability analysis for impulsive Cohen-Grossberg neural networks with time-varying delays and distributed delays,” Nonlinear Analysis. Real World Applications, vol. 10, no. 5, pp. 2784-2798, 2009. · Zbl 1162.92002 · doi:10.1016/j.nonrwa.2008.08.005